Heterogeneous Volume Modelling and Variable Microstructures Speaker: Alexander Pasko Co-authors: Turlif Vilbrandt, Oleg Fryazinov, Pierre-Alain Fayolle, Valery Adzhiev Bournemouth University-Uformia AS-University of Aizu UK-Norway-Japan Geometric Modelling Meeting Seoul 2011
Outline Heterogeneous objects modelling Natural and artificial microstructures Problems with surfaces & voxels Using real functions Regular and non-regular procedural microstructures Direct rendering and fabrication
Dragon ’ s secret
Challenge of Nature Modeling & Fabricating
Heterogeneous objects Internal structure with non-uniform volumetric distribution of properties (density, color, transparency, etc.) Entities of different dimensionalities Gradually varying material distribution in CAD/CAM and fabrication Physical simulations, geological and medical modeling and rendering
Natural and artificial microstructures
Problems with surfaces & voxels Size and processing time - 100s Mb polygons, >10 10 voxels Validity and precision - cracks and approximations Parameterization and operability - blends, offsets, deformations Manufacturability - STL problems are amplified by the geometric complexity of microstructures
Constructive Hypervolume Model Hypervolume is a multidimensional point set with multiple attributes o = ( F ( F(X) X), S 1 (X), …, S k k (X) X) ) F(X) X) – FRep of geometry S i i (X) X) – attributes based on FRep space partitions Graphical Models, 2001
Function Representation FRep Uniform representation of multidimensional point sets as ) 0 F( X ) Function F(X) evaluation procedure traversing the construction tree structure Leaves: primitives Nodes: operations + relations Visual Computer, 1995
Procedural microstructures Procedural generation of the defining function F( X ) X ) value at the given point such that geometry of the entire microstructure is described as X ) 0 F( X ) Constructive model based on R-functions: Graphical Models, 2011
Regular infinite lattices Periodic infinite slabs Rods: intersection of slabs Lattice: union of rods
Variations of lattices Variable rod thickness Smoothed rods
Combining with a shell Truncation of a lattice by Blending union between a solid and union with rods and with a shell its shell
Parameterization by distance Lattice step decreases closer to the surface
Cellular microstructures Replication of a unit cell with periodic space mapping: x’ = sawtooth(x) Non-symmetric cell Symmetric cell
Space-variant structures Transfinite interpolation between cellular structures Computer-Aided Design, 2011
Multi-scale nested structures comment
Filter design
Lattice scaffold for a jaw bone Initial jaw bone model Union of lattice with bone shell Lattice truncated by bone Jaw bone model by Denis Kravtsov
Porous media 1. Basic pore replication 2. Distance dependency 3. Adding noise
Direct rendering Real-time ray-tracing on GPU independent of the microstructure density Computers & Graphics, 2010
Towards direct fabrication 3D Systems Sinterstation ZCorp 3D printer Stratasys Dimension STL problems 3D prints by the Centro de Proprietary protocols Tecnologia da Informao, CTI, Brasil
Graded cellular behavior Auxetic foam by Prof. Norbert Palz Universität der Künste Berlin UDK
Fab@Home HyperFun Printer Direct output from FRep models Too low resolution for microstructures
Direct multimaterial fabrication
Next: gradient volumetric materials
Conclusions Polygon-free and voxel-free approach to Interactive modeling Real-time rendering Fabrication (ongoing) Fitting and analysis (future work) Step towards procedural multiresolution modeling on micro- and nano-levels with infinite “zoom”.
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